相关论文: Complex coordinate rotation method based on gradie…
Distributionally robust optimization (DRO) problems are increasingly seen as a viable method to train machine learning models for improved model generalization. These min-max formulations, however, are more difficult to solve. We therefore…
The constrained gradient method (CGM) has recently been proposed to solve convex optimization and monotone variational inequality (VI) problems with general functional constraints. While existing literature has established convergence…
We propose a novel gradient-based online optimization framework for solving stochastic programming problems that frequently arise in the context of cyber-physical and robotic systems. Our problem formulation accommodates constraints that…
In this paper, acceleration of gradient methods for convex optimization problems with weak levels of convexity and smoothness is considered. Starting from the universal fast gradient method which was designed to be an optimal method for…
Atomic orbitals underpin our understanding of electronic structure, providing intuitive descriptions of bonding, charge transfer, magnetism, and correlation effects. Despite their utility, an atomic basis that is adaptable, strictly…
A recent article introduced thecontinuous stochastic gradient method (CSG) for the efficient solution of a class of stochastic optimization problems. While the applicability of known stochastic gradient type methods is typically limited to…
A new technique of global optimization and its applications in particular to neural networks are presented. The algorithm is also compared to other global optimization algorithms such as Gradient descent (GD), Monte Carlo (MC), Genetic…
The conjugate gradient (CG) method is an efficient iterative method for solving large-scale strongly convex quadratic programming (QP). In this paper we propose some generalized CG (GCG) methods for solving the $\ell_1$-regularized…
Gradient-based trajectory optimization (GTO) has gained wide popularity for quadrotor trajectory replanning. However, it suffers from local minima, which is not only fatal to safety but also unfavorable for smooth navigation. In this paper,…
Designing a fast and efficient optimization method with local optima avoidance capability on a variety of optimization problems is still an open problem for many researchers. In this work, the concept of a new global optimization method…
In this paper, we study a conjugate gradient method for electronic structure calculations. We propose a Hessian based step size strategy, which together with three orthogonality approaches yields three algorithms for computing the ground…
We devise a new accelerated gradient-based estimating sequence technique for solving large-scale optimization problems with composite structure. More specifically, we introduce a new class of estimating functions, which are obtained by…
We developed a general theoretical approach and a user-ready computer code that permit to study the dynamics of collisional energy transfer and ro-vibrational energy exchange in complex molecule-molecule collisions. The method is a mixture…
The complex scaling method (CSM) is a useful similarity transformation of the Schr\"odinger equation, in which bound-state spectra are not changed but continuum spectra are separated into resonant and non-resonant continuum ones. Because…
In machine learning, nonconvex optimization problems with multiple local optimums are often encountered. Graduated Optimization Algorithm (GOA) is a popular heuristic method to obtain global optimums of nonconvex problems through…
In this contribution, we present a full overview of the continuous stochastic gradient (CSG) method, including convergence results, step size rules and algorithmic insights. We consider optimization problems in which the objective function…
A collision-based hybrid algorithm for the discrete ordinates approximation of the neutron transport equation is extended to the multigroup setting. The algorithm uses discrete energy and angle grids at two different resolutions and…
Traditional clustering algorithms often struggle with high-dimensional and non-uniformly distributed data, where low-density boundary samples are easily disturbed by neighboring clusters, leading to unstable and distorted clustering…
This paper presents a fast method for global search of atomic structures at ab initio level. The structures global optimization (SGO) engine consists of a high-efficiency differential evolution algorithm, accelerated local relaxation…
Computed tomography (CT) is an important imaging technique used in medical analysis of the internal structure of the human body. Previously, image segmentation methods were required after acquiring reconstructed CT images to obtain…